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Proof step 7 from proof abs-dirs-trunc (previous step)

fs[ri[inodekey(ino)]].directory, inodekey(ino) ∈ ri ⊦ adr ∈ ri, fs[ri[inodekey(ino)]].meta = fs[adr, truncnode(key, n)][ri[inodekey(ino)]].meta ∧ fs[ri[inodekey(ino)]].size = fs[adr, truncnode(key, n)][ri[inodekey(ino)]].size ∧ fs[ri[inodekey(ino)]].nlink = fs[adr, truncnode(key, n)][ri[inodekey(ino)]].nlink ∧ fs[ri[inodekey(ino)]].nsubdirs = fs[adr, truncnode(key, n)][ri[inodekey(ino)]].nsubdirs ∧ abs-children(ino, fs, ri) = abs-children(ino, fs[adr, truncnode(key, n)], ri)

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 8:
fs[ri[inodekey(ino)]].directory, inodekey(ino) ∈ ri ⊦ ri[inodekey(ino)] = adr, adr ∈ ri, fs[ri[inodekey(ino)]].meta = fs[adr, truncnode(key, n)][ri[inodekey(ino)]].meta ∧ fs[ri[inodekey(ino)]].size = fs[adr, truncnode(key, n)][ri[inodekey(ino)]].size ∧ fs[ri[inodekey(ino)]].nlink = fs[adr, truncnode(key, n)][ri[inodekey(ino)]].nlink ∧ fs[ri[inodekey(ino)]].nsubdirs = fs[adr, truncnode(key, n)][ri[inodekey(ino)]].nsubdirs ∧ abs-children(ino, fs, ri) = abs-children(ino, fs[adr, truncnode(key, n)], ri)

Rule argument

fma: ri[inodekey(ino)] = adr

Additional information

Used simplifier rules: key ∈ ri ⊦ ri[key] ∈ ri; (s) Used formulas: ri[inodekey(ino)] = adr